Answers:
- Variance = 3
- Standard Deviation = Exactly
which approximates to 1.73205
I'm using the population version of each item.
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Step-by-step explanation:
I'll assume your teacher wants the population variance and population standard deviation.
The first task is to add the values up
-2 + 1 + (-1) + 2 + (-3) + 0 + 2 + 1 = 0
Divide that sum over the number of values in the set (n = 8)
0/8 = 0
The mean is 0.
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The next step is to subtract the mean from each value. Luckily the mean is 0 so it won't change any of the values from the given data set.
But if you really wanted, you could have -2-0 = -2, 1-0 = 1, and so on.
Afterward, square each result
- (-2)^2 = 4
- 1^2 = 1
- (-1)^2 = 1
- 2^2 = 4
- (-3)^2 = 9
- 0^2 = 0
- 2^2 = 4
- 1^2 = 1
Adding these squares gets us
4+1+1+4+9+0+4+1 = 24
This is the Sum of the Squared Errors (SSE). Each error is the distance or difference a value is from the mean. The "squared" part should be fairly self explanatory, as well as the "sum" part also.
Divide this SSE value by the sample size n = 8
SSE/n = 24/8 = 3
This is the population variance. To get the sample variance, divide the SSE over n-1 instead of n.
Apply the square root to the variance to get the standard deviation.
So the standard deviation is exactly
which approximates to roughly 1.73205
Both variance and standard deviation are a measure how spread out a data set is.